# Size of variable arrays:
sizeAlgebraic = 13
sizeStates = 6
sizeConstants = 21
from math import *
from numpy import *

def createLegends():
    legend_states = [""] * sizeStates
    legend_rates = [""] * sizeStates
    legend_algebraic = [""] * sizeAlgebraic
    legend_voi = ""
    legend_constants = [""] * sizeConstants
    legend_voi = "t in component environment (second)"
    legend_constants[0] = "C_m in component environment (fF)"
    legend_algebraic[7] = "v_RyR in component RyR (fmol_per_sec)"
    legend_constants[1] = "F in component constants (C_per_mol)"
    legend_states[0] = "q_Ca_SR in component environment (fmol)"
    legend_states[1] = "q_Ca_D in component environment (fmol)"
    legend_states[2] = "q_C_RyR in component environment (fmol)"
    legend_states[3] = "q_CI_RyR in component environment (fmol)"
    legend_states[4] = "q_I_RyR in component environment (fmol)"
    legend_states[5] = "q_O_RyR in component environment (fmol)"
    legend_algebraic[12] = "v_RyRgate_Ca_D in component RyR (fmol_per_sec)"
    legend_constants[2] = "kappa_RyR in component RyR_parameters (fmol_per_sec)"
    legend_constants[3] = "kappa_OC in component RyR_parameters (fmol_per_sec)"
    legend_constants[4] = "kappa_CCI in component RyR_parameters (fmol_per_sec)"
    legend_constants[5] = "kappa_CII in component RyR_parameters (fmol_per_sec)"
    legend_constants[6] = "kappa_IO in component RyR_parameters (fmol_per_sec)"
    legend_constants[7] = "K_Ca_SR in component RyR_parameters (per_fmol)"
    legend_constants[8] = "K_Ca_D in component RyR_parameters (per_fmol)"
    legend_constants[9] = "K_C_RyR in component RyR_parameters (per_fmol)"
    legend_constants[10] = "K_CI_RyR in component RyR_parameters (per_fmol)"
    legend_constants[11] = "K_I_RyR in component RyR_parameters (per_fmol)"
    legend_constants[12] = "K_O_RyR in component RyR_parameters (per_fmol)"
    legend_constants[13] = "R in component constants (J_per_K_per_mol)"
    legend_constants[14] = "T in component constants (kelvin)"
    legend_constants[15] = "nCa_1 in component RyR (dimensionless)"
    legend_constants[16] = "nCa_2 in component RyR (dimensionless)"
    legend_algebraic[0] = "mu_Ca_SR in component RyR (J_per_mol)"
    legend_algebraic[2] = "mu_Ca_D in component RyR (J_per_mol)"
    legend_algebraic[1] = "q_Ca_gate_complexes in component RyR (fmol)"
    legend_algebraic[3] = "mu_C_RyR in component RyR (J_per_mol)"
    legend_algebraic[4] = "mu_CI_RyR in component RyR (J_per_mol)"
    legend_algebraic[5] = "mu_I_RyR in component RyR (J_per_mol)"
    legend_algebraic[6] = "mu_O_RyR in component RyR (J_per_mol)"
    legend_algebraic[8] = "v_OC in component RyR (fmol_per_sec)"
    legend_algebraic[9] = "v_CCI in component RyR (fmol_per_sec)"
    legend_algebraic[10] = "v_CII in component RyR (fmol_per_sec)"
    legend_algebraic[11] = "v_IO in component RyR (fmol_per_sec)"
    legend_constants[17] = "zNa in component ion_valences (dimensionless)"
    legend_constants[18] = "zCl in component ion_valences (dimensionless)"
    legend_constants[19] = "zK in component ion_valences (dimensionless)"
    legend_constants[20] = "zCa in component ion_valences (dimensionless)"
    legend_rates[0] = "d/dt q_Ca_SR in component environment (fmol)"
    legend_rates[1] = "d/dt q_Ca_D in component environment (fmol)"
    legend_rates[5] = "d/dt q_O_RyR in component environment (fmol)"
    legend_rates[2] = "d/dt q_C_RyR in component environment (fmol)"
    legend_rates[3] = "d/dt q_CI_RyR in component environment (fmol)"
    legend_rates[4] = "d/dt q_I_RyR in component environment (fmol)"
    return (legend_states, legend_algebraic, legend_voi, legend_constants)

def initConsts():
    constants = [0.0] * sizeConstants; states = [0.0] * sizeStates;
    constants[0] = 1.381e5
    constants[1] = 96485
    states[0] = 6.41e-1
    states[1] = 3.68876E-07
    states[2] = 2.9682830E-06
    states[3] = 2.9682830E-06
    states[4] = 2.9682830E-06
    states[5] = 2.9682830E-06
    constants[2] = 498020
    constants[3] = 5.01701
    constants[4] = 6.61466
    constants[5] = 5.43605
    constants[6] = 0.453004
    constants[7] = 102.047
    constants[8] = 66.2643
    constants[9] = 0.819033
    constants[10] = 0.755897
    constants[11] = 11.0374
    constants[12] = 11.9593
    constants[13] = 8.31
    constants[14] = 310
    constants[15] = 1
    constants[16] = 2
    constants[17] = 1
    constants[18] = -1
    constants[19] = 1
    constants[20] = 2
    return (states, constants)

def computeRates(voi, states, constants):
    rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic
    algebraic[0] = constants[13]*constants[14]*log(constants[7]*states[0])
    algebraic[2] = constants[13]*constants[14]*log(constants[8]*states[1])
    algebraic[6] = constants[13]*constants[14]*log(constants[12]*states[5])
    algebraic[7] = constants[2]*exp(algebraic[6]/(constants[13]*constants[14]))*(exp(algebraic[0]/(constants[13]*constants[14]))-exp(algebraic[2]/(constants[13]*constants[14])))
    rates[0] = -algebraic[7]
    algebraic[3] = constants[13]*constants[14]*log(constants[9]*states[2])
    algebraic[8] = constants[3]*(exp(algebraic[6]/(constants[13]*constants[14]))-exp((algebraic[3]+constants[16]*algebraic[2])/(constants[13]*constants[14])))
    algebraic[4] = constants[13]*constants[14]*log(constants[10]*states[3])
    algebraic[9] = constants[4]*(exp((algebraic[3]+constants[15]*algebraic[2])/(constants[13]*constants[14]))-exp(algebraic[4]/(constants[13]*constants[14])))
    rates[2] = algebraic[8]-algebraic[9]
    algebraic[5] = constants[13]*constants[14]*log(constants[11]*states[4])
    algebraic[10] = constants[5]*(exp((algebraic[4]+constants[16]*algebraic[2])/(constants[13]*constants[14]))-exp(algebraic[5]/(constants[13]*constants[14])))
    rates[3] = algebraic[9]-algebraic[10]
    algebraic[11] = constants[6]*(exp(algebraic[5]/(constants[13]*constants[14]))-exp((algebraic[6]+constants[15]*algebraic[2])/(constants[13]*constants[14])))
    rates[5] = algebraic[11]-algebraic[8]
    rates[4] = algebraic[10]-algebraic[11]
    algebraic[12] = ((constants[16]*algebraic[8]-constants[15]*algebraic[9])-constants[16]*algebraic[10])+constants[15]*algebraic[11]
    rates[1] = algebraic[7]+algebraic[12]
    return(rates)

def computeAlgebraic(constants, states, voi):
    algebraic = array([[0.0] * len(voi)] * sizeAlgebraic)
    states = array(states)
    voi = array(voi)
    algebraic[0] = constants[13]*constants[14]*log(constants[7]*states[0])
    algebraic[2] = constants[13]*constants[14]*log(constants[8]*states[1])
    algebraic[6] = constants[13]*constants[14]*log(constants[12]*states[5])
    algebraic[7] = constants[2]*exp(algebraic[6]/(constants[13]*constants[14]))*(exp(algebraic[0]/(constants[13]*constants[14]))-exp(algebraic[2]/(constants[13]*constants[14])))
    algebraic[3] = constants[13]*constants[14]*log(constants[9]*states[2])
    algebraic[8] = constants[3]*(exp(algebraic[6]/(constants[13]*constants[14]))-exp((algebraic[3]+constants[16]*algebraic[2])/(constants[13]*constants[14])))
    algebraic[4] = constants[13]*constants[14]*log(constants[10]*states[3])
    algebraic[9] = constants[4]*(exp((algebraic[3]+constants[15]*algebraic[2])/(constants[13]*constants[14]))-exp(algebraic[4]/(constants[13]*constants[14])))
    algebraic[5] = constants[13]*constants[14]*log(constants[11]*states[4])
    algebraic[10] = constants[5]*(exp((algebraic[4]+constants[16]*algebraic[2])/(constants[13]*constants[14]))-exp(algebraic[5]/(constants[13]*constants[14])))
    algebraic[11] = constants[6]*(exp(algebraic[5]/(constants[13]*constants[14]))-exp((algebraic[6]+constants[15]*algebraic[2])/(constants[13]*constants[14])))
    algebraic[12] = ((constants[16]*algebraic[8]-constants[15]*algebraic[9])-constants[16]*algebraic[10])+constants[15]*algebraic[11]
    algebraic[1] = constants[16]*states[5]+constants[15]*states[3]+(constants[15]+constants[16])*states[4]
    return algebraic

def solve_model():
    """Solve model with ODE solver"""
    from scipy.integrate import ode
    # Initialise constants and state variables
    (init_states, constants) = initConsts()

    # Set timespan to solve over
    voi = linspace(0, 10, 500)

    # Construct ODE object to solve
    r = ode(computeRates)
    r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1)
    r.set_initial_value(init_states, voi[0])
    r.set_f_params(constants)

    # Solve model
    states = array([[0.0] * len(voi)] * sizeStates)
    states[:,0] = init_states
    for (i,t) in enumerate(voi[1:]):
        if r.successful():
            r.integrate(t)
            states[:,i+1] = r.y
        else:
            break

    # Compute algebraic variables
    algebraic = computeAlgebraic(constants, states, voi)
    return (voi, states, algebraic)

def plot_model(voi, states, algebraic):
    """Plot variables against variable of integration"""
    import pylab
    (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends()
    pylab.figure(1)
    pylab.plot(voi,vstack((states,algebraic)).T)
    pylab.xlabel(legend_voi)
    pylab.legend(legend_states + legend_algebraic, loc='best')
    pylab.show()

if __name__ == "__main__":
    (voi, states, algebraic) = solve_model()
    plot_model(voi, states, algebraic)